A raster Voronoi diagram generation algorithm based on horizontal-longitudinal scanning

• Main Authors: LIU Qingping, ZHAO Xuesheng, WANG Lei, SUN Wenbin
• Format: Article
• Language: zho
• Published: Surveying and Mapping Press 2019-03-01
• Series: Acta Geodaetica et Cartographica Sinica
• Subjects: Voronoi diagram; raster scan; raster distance
• Online Access: http://html.rhhz.net/CHXB/html/2019-3-393.htm

The Voronoi diagram is an important data structure in computational geometry and has a wide range of applications in many fields. The scan algorithm of raster is an optimization of the Euclidean distance algorithm, which is in line with the discrete features of computers. It is one of the optimal algorithms for the generation of raster Voronoi diagram. However, due to the difference between the grid distance and the Euclidean distance, the ownership of some grids in the scanning process inevitably has some errors, so that the application of the raster Voronoi diagram is limited. In this paper, according to the characteristics of error existing in traditional scanning algorithms, an improved algorithm for the generation of raster Voronoi diagram based on horizontal-longitudinal scanning is proposed. First of all, the causes and the regional distribution characteristics of defects of the traditional scanning algorithm are analyzed in depth. Then, using the 3×3 neighborhood as a template, a vertical scan is added after a horizontal scan. That is to say, the Voronoi diagram can be generated accurately by horizontal and vertical scanning. Finally, different raster data are used to carry out experimental comparison. The results show that the improved algorithm not only has the advantage of efficiency of scanning algorithm, but also solves the error of the original algorithm. It keeps the efficiency while limiting the error to a grid.